Is x = 0 a valid potential solution to the equation log(x + 7) + log(x − 3) = 17? Question 9 options: A) No, because it isn't possible to take the logarithm of zero: log(0). B) No, because when x = 0, the second term is log(− 3), and it's impossible to take the logarithm of a negative number. C) Yes, logarithms are valid for any integer. D) No, because 17 isn't divisible by 7 or 3.

Answer:

Step-by-step explanation:

slant height l = 14cm

r = 6 cm

Use Pythagorean theorem.

h² + 6² = 14²

h² + 36 = 196

h² = 196 - 36

h² = 160

h = √160

h = 12.65 cm

[tex]Volume=\frac{1}{3}\pi r^{2}h\\\\=\frac{1}{3}*3.14*6*6*12.64\\\\[/tex]

= 476.61 cubic cm

Answer:

The volume of cone is 476.61 cm³.

Step-by-step explanation:

Solution :

As per given question we have provided :

[tex]\begin{gathered}\end{gathered}[/tex]

Firstly, finding the height of cone by substituting the values in the formula :

[tex]{\longrightarrow{\pmb{\sf{l = \sqrt{(r)^{2} + {(h)}^{2} }}}}}[/tex]

Substituting all the given values in the formula to find the height of cone :

[tex]\begin{gathered}\begin{array}{l}\quad{\longrightarrow{\sf{l = \sqrt{(r)^{2} + {(h)}^{2}}}}}\\\\\quad{\longrightarrow{\sf{{(l)}^{2} =(r)^{2} + {(h)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(14)}^{2} =(6)^{2} + {(h)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(14 \times 14)} =(6 \times 6) + {(h)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(196)} =(36) + {(h)}^{2}}}}\\\\\quad{\longrightarrow{\sf{ {(h)}^{2} = 196 - 36}}}\\\\\quad{\longrightarrow{\sf{ {(h)}^{2} = 160}}}\\\\\quad{\longrightarrow{\sf{h = \sqrt{160}}}}\\\\\quad{\longrightarrow{\sf{h = 12.65}}}\\\\\quad{\star{\underline{\boxed{\sf{\purple{h = 12.65}}}}}} \end{array}\end{gathered}[/tex]

Hence, the height of cone is 12.65 cm.

[tex]\begin{gathered}\end{gathered}[/tex]

Now, finding the volume of cone by substituting the values in the formula :

[tex]\longrightarrow{\pmb{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}}[/tex]

Substituting all the given values in the formula to find the volume of cone :

[tex]\begin{gathered}\begin{array}{l}\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14{(6)}^{2} 12.65}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14{(6 \times 6)}12.65}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14{(36)}12.65}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = \dfrac{1}{\cancel{3}}\times 3.14 \times \cancel{36}\times 12.65}}\\\\\quad\longrightarrow{\sf{Volume_{(Cone)} = 3.14 \times 12 \times 12.65}}\\ \\\quad\longrightarrow{\sf{Volume_{(Cone)} = 476.61 \: {cm}^{3}}}\\\\\quad\star{\underline{\boxed{\sf{\pink{Volume_{(Cone)} = 476.61 \: {cm}^{3}}}}}}\end{array}\end{gathered}[/tex]

Hence, the volume of cone is 476.61 cm³.

[tex]\rule{300}{2.5}[/tex]

Answer:

p=72-b

Step-by-step explanation:

From the statement, you can say that the number of people whom supplies will be provided would be equal to the number of people that travel to the beach minus the amount of people that bring their own supplies:

p=72-b, where:

p= number of people for whom supplies will be provided

b= number of people that bring their own supplies

Answer:

A total of 720 elk are likely to be infected

Step-by-step explanation:

we shall be using the proportion by survey to estimate the number of infections

From the survey 8 out of 50 are infected. Thus the likelihood of infection is 8/50

We have 4,500 elk to consider. The number of elk likely to be infected will be 8/50 * 4500 = 720

Based on the sample proportion, it is estimated that approximately 880 elk out of the 5,500 elk in the wildlife preserve are infected with the parasite.

Step 1

To estimate the number of elk likely to be infected with a parasite at a wildlife preserve, we use the sample proportion to project the infection rate to the entire population.

Given:

- Total population of elk [tex]\( N = 5500 \)[/tex]

- Sample size [tex]\( n = 50 \)[/tex]

- Number of infected elk in the sample [tex]\( x = 8 \)[/tex]

First, we calculate the sample proportion [tex]\( \hat{p} \)[/tex]:

[tex]\[ \hat{p} = \frac{x}{n} = \frac{8}{50} = 0.16 \][/tex]

This sample proportion represents the estimated infection rate. To estimate the number of infected elk in the entire population, we multiply this proportion by the total population:

[tex]\[ \text{Estimated number of infected elk} = \hat{p} \times N \][/tex]

Step 2

Substituting the values:

[tex]\[ \text{Estimated number of infected elk} = 0.16 \times 5500 \][/tex]

Performing the calculation:

[tex]\[ \text{Estimated number of infected elk} = 0.16 \times 5500 = 880 \][/tex]

So, approximately 880 elk in the wildlife preserve are likely to be infected with the parasite.

Complete question : Part of the population of 5,500 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected.

How many elk are likely to be infected?

The answer would be that by excluding the outlier, a better description can be given for the data set. This would be because that the plant might grow very very slowly since it depends on the type of plant it is or other factors that might attribute to it.

Answer:

Step-by-step explanation:

hello :

7w+3-3 =24-3

7w=21

w=21/7 =3

Answer:

42

Step-by-step explanation:

7 x 3 x 2 = 42

Answer:

c: 95%

Step-by-step explanation:

got it right on ed

Using the Empirical Rule, it is found that about 95% of the data lies within 2 standard deviations of the mean in a normal distribution.

It states that, for a normally distributed random variable:

Hence, 95% is the answer for this question.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

Answer:

46

Step-by-step explanation:

a:3, b:2 , c: 7 and d:4

ab + 5c - d

(3*5) + 5(7) - 4

(15 + 35) -4

50- 4 :46

Answer:

37.

Step-by-step explanation:

ab + 5c - d

= 3*2 + 5*7 - 4

= 6 + 35 - 4

= 37.

The students spent 5% of their $500 budget on props, calculated by dividing $25 by $500 and then multiplying by 100.

To determine the percentage of the total budget that was spent on props for the student film, we need to use the formula for calculating percentages. The formula is
(amount spent / total budget)
* 100 = percentage spent.

Applying this formula to the given values:

Therefore, the students spent 5% of their total budget on props.

Answer:

Step 3

Reason:

I toke the test/review.

Answer:

the and should be step 3

Step-by-step explanation:

Answer:

There will be $2288.98 in the account after 6 years

Step-by-step explanation:

We are given that $1750 is put into an account that pays an annual rate of 4.5%  compounded quarterly.

So, Principal = $1750

Rate of interest = 4.5%

No. of compounds per year = 4

Time = 6 years

Formula :[tex]A =P(1+\frac{r}{n})^{nt}[/tex]

Where A = Amount

P = Principal

r = rate of interest

n = no. of compounds per year

t = time

Substitute the values in the formula :

[tex]A =1750(1+\frac{4.5}{400})^{4 \times 6}[/tex]

A=2288.98

Hence There will be $2288.98 in the account after 6 years

Final answer:

To find the numbers Ali picked, we identify the lowest number (11), calculate the highest number using the range (11 + 13 = 24), and confirm that the median (17) fits between these two numbers. Thus, the numbers are 11, 17, and 24.

Explanation:

Ali picked three numbers, and we have been provided with three pieces of information about these numbers: the lowest number was 11, the range was 13, and the median was 17. We can use this information to determine the three numbers Ali picked.

Step 1: Identify the Lowest Number

We know the lowest number is 11. This is our starting point.

Step 2: Determine the Range

The range of a set of numbers is the difference between the highest and the lowest numbers. Since the range is 13, we add this to the lowest number to find the highest number: 11 + 13 = 24. So, the highest number Ali picked is 24.

Step 3: Find the Median

The median is the middle number in a set of numbers that has been arranged in order. We are told the median is 17, which fits perfectly between our lowest and highest numbers, confirming that our calculations are correct.

Therefore, the numbers Ali picked, in order from lowest to highest, are: 11, 17, and 24.

Answer:

$534

Step-by-step explanation:

Simple Interest formula:   I = Prt

I = $890 * (0.05)* 12

I = $534

Answer:

Step-by-step explanation:

534

Answer:

q= 6

Step-by-step explanation

Answer:

6

Step-by-step explanation:

6+7q =48

7q= 48-6

7q= 42

q=42/7

q= 6

Answer: False wouldn't it be -100 dollars if hes buying something. Correct me if im wrong.

Hey there :)

To find the slope with two points we will need to use the equation  [tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

[tex]x^1[/tex]    [tex]x^2[/tex]       [tex]y^1[/tex]  [tex]y^2[/tex]

( 3 , -20 )  ( 5 , 8 )

Here is what the equation should look like when replaced with the numbers (it will be a fraction) :

                                     [tex]\frac{8 - (-20)}{5 - 3}[/tex]

We know that two negatives cancel out and make a positive, so the numerator would actually be 8 + 20.

Solve the fraction and we get   [tex]\frac{28}{2}[/tex]

28 divided by 2 is 14. The slope is 14.

Answer:

1/4

Step-by-step explanation:

Just did this.

Answer:

6a - 18

Step-by-step explanation:

[tex]6(a - 3) \\ = 6 \times a - 6 \times 3 \\ = 6a - 18[/tex]

Answer:

The answer is B. 6(a)-6(3)

Step-by-step explanation:

I took quiz and got 100%

Answer:

B

Step-by-step explanation:

it adds up to 185

Answer: c on edg

Step-by-step explanation: I have no idea, i guess that’s just what it is, I’m no math genius.

Lines and points are both undefined terms in geometry.

The diagram that represents the postulate is line (c)

The given postulate states that:

Exactly one line exists between any two points.

This means that:

The line must pass through the two points.

From the given options (see attachment)'

Only option (c) is true

Because the line passes through points A and B.

Hence, the diagram that supports the postulate is line (c).

Read more about points and lines at:

https://brainly.com/question/15212542

First, let us break down 28 hours 36 minutes into minutes.

Number of minutes taken to grade 220 essays = (28 x 60) + 36 = 1680 + 36 = 1716 minutes

Now, we can find the average time taken to grade an essay by dividing the time taken to grade 220 essays by 220.

Average amount of time taken to grade an essay = [tex]\frac{1716}{220}[/tex] = 7.8 minutes, or 7 minutes and 48 seconds

Answer:

(x+4)(x-5)

Step-by-step explanation:

You need to find two numbers that multiply to be -20 but add up to be -1.

Answer:

( x - 5 ) ( x + 4 )

Step-by-step explanation:

When solving quadratic equations it's important to remember that they have 2 solution. We need to work out the factors, sum and the products to successfully factorise the quadratic and solve it. So,

x² - x - 20 = 0

Sum = -1

Product = -20

So we need two numbers that sum to -1 and multiply together to make -20

Factors = -5 and 4

x² - 5x + 4x - 20

Factor x² - 5x and 4x -20 separately

x² - 5x = x ( x - 5 )

4x - 20 = 4 ( x - 5 ) So

x ( x - 5 ) + 4 ( x - 5 )

We can see a common factor of  ( x - 5 ) and the other bracket would be       ( x + 4)

( x - 5 ) ( x + 4 )

Answer:

The spinner has 6 equal-sized slices, so each slice has a 1/6 probability of showing up.

I guess that we want to find the expected value in one spin:

number 1: wins $1

number 2: wins $3

number 3: wins $5

number 4: wins $7

number 5: losses $8

number 6: loses $8

The expected value can be calculated as:

Ev = ∑xₙpₙ

where xₙ is the event and pₙ is the probability.

We know that the probability for all the events is 1/6, so we have:

Ev = ($1 + $3 + $5 + $7 - $8 - $8)*(1/6) = $0

So the expected value of this game is $0, wich implies that is a fair game.

The question is a probability problem in Mathematics. It requires calculating the expected value of a game based on the potential winnings and losses and their respective probabilities. On average, Ivanna will lose a dollar each time she plays.

The subject matter of this question is a probability problem within Mathematics. One way to approach the problem would be to calculate the expected value of Ivanna's winnings from a single spin of the spinner. Each outcome (1, 2, 3, 4, 5, 6) has an equal chance of being chosen, which is 1/6, because there are 6 equally likely outcomes.

The formula for the expected value is the sum of all potential outcomes multiplied by their respective probabilities. Numerically, this would be (1*$1 + 1*$3 + 1*$5 + 1*$7 - 2*$8) / 6, which equals -$1.

Therefore, on average, Ivanna will lose a dollar each time she plays this game.

https://brainly.com/question/35639289

#SPJ3

Answer:

A and C

Step-by-step explanation:

w+c must be up to (<=) 41. corn must be less than (<) 28.

Answer:

Yes

Step-by-step explanation:

the given function is exponential, because x is the exponent of 3

Answer:

2x

Step-by-step explanation:

if x equals the amount of miles per hour, then 2x would equal the amount of miles in 2 hours